Suppose that the random variable Y has a gamma
Chapter 8, Problem 39E(choose chapter or problem)
Suppose that the random variable Y has a gamma distribution with parameters \(\alpha=2\) and an unknown \(\beta\). In Exercise 6.46, you used the method of moment-generating functions to prove a general result implying that \(2 Y / \beta\) has a \(\chi^{2}\) distribution with 4 degrees of freedom (df). Using \(2 Y / \beta\) as a pivotal quantity, derive a 90% confidence interval for \(\beta\).
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